Algorithms and Complexity of Algebraic Problems: This subproject focuses on algebraic problems, more precisely on identity testing problems, arithmetic circuit lower bounds, and isomorphism problems. These are highly relevant problems in current research in theoretical computer science.

Provably Efficient Preprocessing Algorithms: The focus of this subproject is on parameterized complexity, more specifically, on kernelization complexity of problems that are fixed parameter tractable. Using tools from parameterized complexity and combinatorics we plan to derive new upper and lower bounds on the kernel sizes for several concrete problems and devise new techniques and tools to obtain upper and lower bounds in general. In particular, we aim to explore deeper connections between extremal graph theory, matroid theory and kernelization for specifc hard problems.